Problem: $ F = \left[\begin{array}{r}0 \\ 0\end{array}\right]$ $ C = \left[\begin{array}{rrr}2 & -2 & 1 \\ 2 & 2 & 0\end{array}\right]$ Is $ F+ C$ defined?
Solution: In order for addition of two matrices to be defined, the matrices must have the same dimensions. If $ F$ is of dimension $( m \times  n)$ and $ C$ is of dimension $( p \times  q)$ , then for their sum to be defined: 1. $ m$ (number of rows in $ F$ ) must equal $ p$ (number of rows in $ C$ ) and 2. $ n$ (number of columns in $ F$ ) must equal $ q$ (number of columns in $ C$ Do $ F$ and $ C$ have the same number of rows? Yes Yes No Yes Do $ F$ and $ C$ have the same number of columns? No Yes No No Since $ F$ has different dimensions $(2\times1)$ from $ C$ $(2\times3)$, $ F+ C$ is not defined.